Alternate Solutions Analysis For Transportation Problems

Abstract

The constraint structure of the transportation problem is so important that the literature is filled with efforts to provide efficient algorithms for solving it. The intent of this work is to present various rules governing load distribution for alternate optimal solutions in transportation problems, a subject that has not attracted much attention in the current literature, with the result that the load assignment for an alternate optimal solution is left mostly at the discretion of the practitioner. Using the Shadow Price theory we illustrate the structure of alternate solutions in a transportation problem and provide a systematic analysis for allocating loads to obtain an alternate optimal solution. Numerical examples are presented to explain the proposed process.